Dual Energy CT Monitoring of the Renal Corticomedullary Sodium Gradient in Swine

Abstract

Objective

To evaluate the feasibility of dual-energy CT (DECT) for monitoring dynamic changes in the renal corticomedullary sodium gradient in swine.

Material and Methods

This study was approved by our Institutional Animal Care and Use Committee. Four water-restricted pigs were CT-scanned at 80 and 140 kVp at baseline and at 5 minute intervals for 30 minutes during saline or furosemide diuresis. The renal cortical and medullary CT numbers were recorded. A DECT basis material decomposition method was used to quantify renal cortical and medullary sodium concentrations and medulla-to-cortex sodium ratios at each time point based on the measured CT numbers. The sodium concentrations and medulla-to-cortex sodium ratios were compared between baseline and at 30 minutes diuresis using paired student t-tests. The medulla-to-cortex sodium ratios were considered to reflect the corticomedullary sodium gradient.

Results

At baseline prior to saline diuresis, the mean medullary and cortical sodium concentrations were 103.8 ± 8.7 and 65.3 ± 1.7 mmol/l, respectively, corresponding to a medulla-to-cortex sodium ratio of 1.59. At 30 minutes of saline diuresis, the medullary and cortical sodium concentrations decreased to 72.3 ± 1.0 and 56.0 ± 1.4 mmol/l, respectively, corresponding to a significantly reduced medulla-to-cortex sodium ratio of 1.29 (P = 0.045). At baseline prior to furosemide diuresis, the mean medullary and cortical sodium concentrations were 110.5 ± 3.6 and 66.7 ± 4.1 mmol/l, respectively, corresponding to a medulla-to-cortex sodium ratio of 1.66. At 30 minutes of furosemide diuresis, the medullary and cortical sodium concentrations decreased to 68.5 ± 0.3 and 58.9 ± 4.0 mmol/l, respectively, corresponding to a significantly reduced medulla-to-cortex sodium ratio of 1.16 (P = 0.026). One of the 4 pigs developed acute tubular necrosis likely related to prolonged hypoxia during intubation prior to the furosemide diuresis experiment. The medulla-to-cortex sodium ratio for this pig, which was excluded from the mean medulla-to-cortex ratio above, was 1.07 at baseline and 1.15 at 30 minutes following the administration of furosemide.

Conclusion

DECT monitoring of dynamic changes in the renal corticomedullary sodium gradient after physiologic challenges is feasible in swine.

Introduction

A primary function of the kidney is to maintain bodily fluid homeostasis by allowing for the conservation and resorption of fluid during periods of fluid restriction, and the excretion of excess fluid through the urine during periods of fluid excess. The modulation of urine concentration is achieved in large part through dynamic changes in the renal medullary interstitial salt concentration. In times of fluid restriction, sodium chloride is actively transported by the Na/K/Cl₂ symporter into the interstitial space of the medulla to create an osmotic gradient that promotes passive water resorption from the plasma filtrate as it travels from the cortex through the medulla into the urinary collecting system. Alterations in the corticomedullary sodium gradient are seen in many pathologic conditions that affect the renal medulla. For example, alteration in this gradient is a hallmark of acute tubular necrosis (ATN), which is the most frequent cause of hospital-acquired acute renal failure (1). Early identification of ATN and its differentiation from other causes of acute renal failure may be clinically difficult, but are essential for the appropriate management of such disease. Early detection of ATN may be greatly aided if the corticomedullary sodium gradient can be measured.

Currently, our tools to measure the renal sodium gradient are very limited. The only established methods to directly measure the sodium gradient have been evaluated in animal kidneys using micropuncture of the medulla (2–5), which is invasive, damaging to tissue, technically demanding, and only performed in rodents. A noninvasive imaging method to evaluate the renal corticomedullary sodium gradient would be highly desirable. Magnetic resonance sodium imaging and spectroscopy have been used to evaluate the sodium gradient in rat and human kidneys (6–9). However, this technique is costly, requires specialized resources, and is only available at very few centers. Dual-energy computed tomography (DECT), on the other hand, is much more widely available. DECT allows for rapid differentiation and quantification of radio-opaque materials (10), and has the potential to evaluate the renal corticomedullary sodium gradient noninvasively by quantifying the relative amount of sodium in the cortex and medulla. DECT is finding increasing value for numerous abdominal imaging applications, including the quantification of liver iron (11, 12), determination of renal stone composition (13–15), and differentiation between iodine contrast and calcified vascular plaques (16). We hypothesized that DECT may also be used to quantify and monitor changes in sodium, which is radio-opaque, in the kidney, and the corticomedullary sodium gradient. Thus, we undertook this pilot study to assess the feasibility of DECT to quantify changes in the renal corticomedullary sodium gradient following physiologic challenges in swine.

Materials and Methods

Animals and procedures

The study protocol was approved by our Institutional Animal Care and Use Committee and performed according to our Laboratory Animal Resource Center guidelines. Four juvenile female pigs (weight range: 15–25 kg; Pork Power, Turlock, CA) were used in the study. Each pig underwent two different diuretic procedures on two consecutive days. To standardize hydration status before the procedures, the pigs did not have access to food or water for 8 hours prior to each procedure. For procedure (1), the pigs underwent DECT scans immediately prior to and during 30 minutes of hydration with 600 ml of 0.9% normal saline. For procedure (2), the pigs underwent DECT scans immediately prior to and for 30 minutes following intravenous administration of 20 mg of furosemide. All 4 pigs had free access to food and water prior to and between the two procedures.

Immediately prior to CT imaging, the pigs were sedated with telazol (2.2–2.4 mg/kg), intubated, and mechanically ventilated. General anesthesia was achieved with continuous isoflurane titrated with oxygen to effect. Venous access was maintained via an 18–20 G catheter into the ear veins while the pigs were under anesthesia. Bladders were catheterized with foley catheters. Each pig underwent baseline DECT scans prior to saline or furosemide diuresis. Furosemide was chosen because it is a commonly utilized diuretic that functions by potent inhibition of the Na/K/Cl₂ symporter in the renal medullary tubules. For saline diuresis, the pigs were given intravenous 100-mL aliquots of 0.9% normal saline every 5 minutes for 30 minutes (total of 600-mL 0.9% normal saline). DECT scans through the pig kidneys were acquired, and bladder urine was collected via catheter at baseline before the start of saline adminstration and every 5 minutes during the 30 minutes administration of intravenous saline. For furosemide diuresis, the pigs were given 20 mg of furosemide intravenously and DECT scans were acquired and bladder urine was collected at baseline and every 5 minutes for 30 minutes after the administration of furosemide. Urine specific gravity was determined immediately following the urine collection using test strips (Chemstrip 10 SG; Roche Labs, South San Francisco, CA). At the end of the 2 day experiments, each pig underwent a contrast enhanced CT through the kidneys.

One of the 4 pig experiments was complicated by ventilation equipment failure for several minutes during intubation on day 2 prior to the furosemide administration, and the pig likely experienced prolonged hypoxia as a result. This pig failed to produce any urine in response to furosemide. The kidneys from this pig were removed and evaluated histopathologically. Of the other 3 pigs that showed expected diuresis following both furosemide and normal saline administration, one was randomly selected to have its kidneys removed and evaluated histopatholgically.

CT Imaging Protocol

All pigs were scanned with a 64-section multidetector-row CT scanner (VCT; GE Healthcare, Milwaukee, WI). Images were acquired through the kidneys at both 80 and 140 kVp using the rotate-rotate method. To minimize motion between the 80 and 140 kVp acquisitions, the kidneys were imaged in the axial mode. Specifically, during each gantry rotation (0.8 second), images through a 2 cm axial section (slice thickness 5-mm, 4 slices) of the kidneys were acquired first at 80 kVp and then at 140 kVp. This was repeated until the entire kidneys were imaged. The entire kidneys were imaged during a single breathhold by disabling the ventilator at the nadir of expiration. Care was taken to prevent any movement or adjustment in the animals’ position once initial scanning had started.

At the end of the 2 day experiment, the pigs underwent a corticomedullary phase CT scan with 5-mm images acquired from the diaphragm to the symphysis pubis at 120 kVp obtained 15 seconds after an intravenous administration of 20-mL bolus of iohexol (Omnipaque 350, at a rate of 3-mL/sec, Nycomed-Amersham, Princeton, NJ). The rest of the scanning parameters were the same as the DECT kidney scans.

Histopathology

Kidneys were removed immediately following euthanasia and tissue blocks containing cortical and medullary tissue were fixed in 1% formalin, then embedded in paraffin. Tissue slides were created, stained with Hematoxylin and Eosin, and evaluated by a pathologist.

Image Analysis

All DECT images were reviewed on a picture archiving and communication system workstation (IMPAX, version 4.5; Afga, Mortsel, Belgium) with a level of 40 and window of 80. Regions of interest (ROIs) were manually placed in the renal cortex and medulla on the unenhanced DECT images, using the corticomedullary phase contrast enhanced images as a reference (Fig. 1). The ROIs were placed at the same location for the baseline and the subsequent DECT scans acquired every 5 minutes for 30 minutes during saline or furosemide diuresis. Five cortical and five medullary ROIs were placed in both the upper pole and lower pole kidneys, with care to avoid areas of obvious artifact, vessels or collecting system. The average ROI size was 0.1-cm².

Fig. 1.

Corticomedullary phase scan of the left kidney in a female juvenile pig (a). The corticomedullary phase image was used as a reference to place regions-of-interest (ROI) in the renal cortex (red) and medulla (blue) on unenhanced dual-energy CT images (b) at 80 and 140 kVp. Care was taken during medullary ROI placement to avoid areas of obvious artifact, vessels or collecting system.

The mean renal cortical and medullary CT numbers (obtained by averaging the ROIs from both the left and right kidneys) were recorded for each pig, at each time point (baseline and subsequent scans), and at each kVp. At each time point, the fractions of sodium in the renal cortex and medulla were calculated from the CT numbers using a previously reported two material basis decomposition method ((17), Appendix 1). For the purpose of this pilot study, the two materials in the kidneys to be decomposed using DECT methods were sodium chloride and renal soft tissue. The sodium fractions were then converted to sodium concentrations in millimole per liter (mmol/l) using the previously reported relationship between sodium concentration and CT numbers ((18), Appendix 2). The medulla-to-cortex sodium ratios were calculated by dividing the sodium concentration in the medulla by that in the cortex for each time point.

Statistical Analysis

Statistical analysis was performed using Microsoft Excel 2003 (Microsoft, Redmond, WA) and statistical software package Stata (Version 8.0, College Station, TX). Paired student t-tests were used to compare the medulla-to-cortex sodium ratios between 1) the baseline scans and the scans obtained at the end of the 30 minutes saline diuresis, and 2) the baseline scans and the scans obtained at 30 minutes following furosemide diuresis. Linear regression analysis was used to determine the relationship between medulla-to-cortex sodium ratios and urine specific gravity. For all tests, a P value of less than .05 was considered significant.

Results

Three of the 4 pigs showed expected diuresis following both saline and furosemide administration on two consecutive days. The 4^th pig showed expected diuresis following saline administration on day 1, but did not show expected diuresis following furosemide administration on day 2. Histopathological analysis of the kidneys from this 4^th pig indicated severe acute tubular necrosis. The data from the furosemide diuresis experiment for the 4^th pig were analyzed separately, and excluded from the calculations for the mean CT number, sodium concentrations, or medulla-to-cortex sodium ratios.

Figure 2 shows the mean CT numbers at 80 kVp in the renal medulla and cortex at baseline and during saline or furosemide diuresis. Using previously published methods (17), the medullary and cortical sodium concentrations, and the medulla-to-cortex sodium ratios were calculated from the measured medullary and cortical CT numbers at both 80 kVp and 140 kVp, at each time point. For the saline diuresis experiment, at baseline, the mean medullary and cortical sodium concentrations were 103.8 ± 8.7 and 65.3 ± 1.7 mmol/l, respectively, corresponding to a medulla-to-cortex sodium ratio of 1.59. Following 30 minutes of saline diuresis, the mean medullary and cortical sodium concentrations decreased to 72.3 ± 1.0 and 56.0 ± 1.4 mmol/l, respectively, corresponding to a significantly decreased medulla-to-cortex sodium ratio of 1.29 (P < 0.05) (Fig. 3a). For the furosemide diuresis experiment, at baseline, the medullary and cortical sodium concentrations were 110.5 ± 3.6 and 66.7 ± 4.1 mmol/l, respectively, corresponding to a medulla-to-cortex sodium ratio of 1.66. Following 30 minutes of furosemide diuresis, the mean medullary and cortical sodium concentrations decreased to 68.5 ± 0.3 and 58.9 ± 4.0 mmol/l, respectively, corresponding to a significantly decreased medulla-to-cortex sodium ratio of 1.16 (P < 0.05) (Fig. 3b).

Fig. 2.

Line graphs demonstrate renal cortical and medullary CT numbers at peak potential setting of 80 kVp (mean ± standard deviation) during (a) saline diuresis, and (b) furosemide diuresis. a) CT numbers versus the quantity of 0.9% normal saline administered. b) CT numbers versus time after intravenous administration of 20-mg furosemide.

Fig. 3.

Line graphs demonstrate renal medulla-to-cortex sodium ratios (mean ± standard deviation), calculated using dual-energy CT basis material decomposition method, during a) saline diuresis and b) furosemide diuresis. a) The medulla-to-cortex sodium ratio decreased significantly from 1.59 ± 0.15 at baseline to 1.29 ± 0.06 at 30 minutes of saline diuresis following administration of 600 cc of 0.9% normal saline (P = 0.045). b) The medulla-to-cortex sodium ratio decreased significantly from 1.66 ± 0.13 at baseline to 1.16 ± 0.19 at 30 minutes following administration of 20 mg of furosemide (P = 0.026).

The mean urinary specific gravity decreased progressively during both saline and furosemide diuresis (Fig. 4). Linear regression analysis revealed a statistically significant correlation between medulla-to-cortex sodium ratios and urinary specific gravity (r²=0.222, P < 0.001).

Fig. 4.

Line graphs demonstrate urinary specific gravity (mean ± standard deviation) during saline and furosemide diuresis.

For the 4^th pig that did not show expected diuresis following furosemide administration, histopathology of the kidneys showed acute tubular necrosis (Fig. 5a). As a comparison, the kidneys from one of the other 3 pigs that showed expected diuresis following both furosemide and saline administration showed normal renal tubules (Fig. 5b). For the pig with acute tubular necrosis, the baseline medullary and cortical sodium concentrations were 77.2 and 71.9 mmol/l, respectively, corresponding to a medulla-to-cortex sodium ratio of 1.07. At 30 minutes following furosemide administration, the medullary and cortical sodium concentrations were 72.8 and 63.1 mmol/l, respectively, corresponding to a medulla-to-cortex sodium ratio of 1.15 (Fig. 6).

Fig. 5.

A) Renal histology of the pig that did not show expected diuresis following furosemide administration. The renal tubules are dilated with epithelial flattening and mild interstitial edema, consistent with acute tubular necrosis. B) Renal histology of one of the pigs that showed expected diuresis following both furosemide and saline administration. The renal tubules are tightly packed and appear normal. (H&E stain, 400x magnification)

Fig. 6.

Line graph demonstrates medulla-to-cortex sodium ratios at baseline and following administration of 20-mg furosemide for the pig that had pathology proven acute tubular necrosis, suspected to be a result of prolonged hypoxia during anesthesia induction.

Discussion

We show that DECT can monitor a progressive decline in the medulla-to-cortex sodium ratio in the course of saline and furosemide diuresis in swine. These changes in the medulla-to-cortex sodium ratios likely reflect the dissipation of the renal corticomedullary sodium gradient, which is the expected response to saline and furosemide administration. These data suggest that dual-energy CT assessment and monitoring of dynamic changes in the renal corticomedullary sodium gradient may be a feasible noninvasive means to assess a critical and previously difficult-to-evaluate aspect of renal function.

A major strength of DECT is the ability to differentiate and quantify imaged materials (10). Different materials attenuate X-ray spectra in characteristic ways, and this property can be exploited by imaging objects twice, once with lower energy and once with higher energy X-ray spectra, to determine the material composition of the imaged voxel based on the CT number ratio. DECT is increasingly utilized, and is finding value in a growing list of applications, including the evaluation of tissue perfusion, liver iron content (11, 12), and renal stone composition (13–15). In our study, we showed that material decomposition for DECT can potentially be applied as a long sought noninvasive means to evaluate dynamic changes in the renal corticomedullary sodium gradient. Of note, the baseline medulla-to-cortex sodium ratios of the swine kidneys in our study were in agreement with previous report of sodium gradient in the rat kidneys using sodium MR imaging (19).

Our findings of progressive decrease in the medulla-to-cortex sodium ratios in the course of diuresis were consistent with the expected reduction of the corticomedullary sodium gradient during diuresis. The observed strong linear correlation between the medulla-to-cortex sodium ratios and the urine specific gravity was also consistent with the expected result of diuresis with decreased renal sodium gradient and corresponding urine dilution. Incidentally, we observed a much reduced baseline medulla-to-cortex sodium ratio and an absence of change in the sodium ratio following furosemide administration in a pig which had pathologically proven ATN. We suspect that the ATN was secondary to prolonged hypoxia due to ventilation equipment failure during intubation. ATN is expected to reduce or abolish the normal corticomedullary sodium gradient. The data from this pig, while anecdotal, lent further support that alteration in renal sodium gradient in renal disease may be measured by DECT.

DECT has distinct advantages over sodium MR imaging in assessing renal sodium gradient. Sodium MR imaging requires specialized resources such as sodium surface coils, and is only available in limited centers. The acquisition time for sodium MR images is long in order to achieve good signal-to-noise ratios. A recent study on renal sodium MR imaging reported typical scan time of 10 minutes for the sodium images and over 4 minutes for the proton images which were used as anatomic references (19). DECT, on the other hand, is much more widely available. The image acquisition time is on the order of 10 to 20 seconds, which allows imaging even in unstable or noncooperative patients. DECT can also provide outstanding high spatial resolution anatomical images at the same time as potentially providing functional information such as renal corticomedullary sodium gradient.

The renal corticomedullary sodium gradient is tightly coupled to renal function. As mentioned previously, acute tubular necrosis, a common cause of acute renal failure, is characterized by the alteration of sodium gradient. Early identification of acute tubular necrosis and its differentiation from other causes of acute renal failure may be clinically difficult, but are essential for the appropriate management of such diseases, either in native or transplanted kidneys. In the native kidneys, blood test (glomerular filtration rate) and urine analysis (fractional excretion of sodium) that are used to assess acute tubular necrosis only measure global and combined functions of both kidneys. One functioning kidney can mask the dysfunction in the other kidney. Additionally, blood and urine analyses may only reveal abnormality after substantial kidney injury has already occurred, therefore delaying diagnosis. Noninvasive measurement of the renal sodium gradient by DECT has the potential to evaluate regional function of each kidney separately, therefore allowing early diagnosis of renal dysfunction. In transplanted kidneys, differentiating acute tubular necrosis from acute rejection in renal allografts in the early posttransplant period is an important clinical problem as treatment for the two conditions is drastically different. Patients are frequently required to undergo allograft biopsy, with associated risks of bleeding or injury to the allograft, in order to determine the etiology of early graft dysfunction. Evaluation of the renal sodium gradient using DECT may therefore facilitate noninvasive differentiation of acute tubular necrosis from other causes of early allograft dysfunction.

Our study has several limitations. First, there was no standard of reference for the corticomedullary sodium gradient in the pigs against which we can compare our calculated medulla-to-cortex sodium ratios. However, the baseline medulla-to-cortex sodium ratios in our study were in agreement with previous report of sodium gradient in the rat kidneys using sodium MR imaging (19). Furthermore, we observed a progressive decrease in the medulla-to-cortex sodium ratios during diuresis, corresponding to the expected decrease in the corticomedullary sodium gradient during diuresis. These data provide strong support that the medulla-to-cortex sodium ratios, calculated using the DECT material decomposition methods, do indeed reflect the corticomedullary sodium gradient. Second, our sample size was small. Nonetheless we observed a significant change in the medulla-to-cortex sodium ratios between baseline and at 30 minutes diuresis. Future studies will be required to confirm our initial observations. Another limitation is that our observation of DECT assessment of medullary sodium derangement in the setting of acute tubular necrosis was only in one pig. While this observation is anecdotal and intuitive, further studies focusing on DECT evaluation in acute tubular necrosis are warranted. Third, we assessed the distribution of the sodium in the kidney by means of ROI-based analysis where we placed ROIs conservatively in the cortex and the medulla. This generated average sodium concentrations in the medulla and the cortex, and the medulla-to-cortex sodium ratios which are an estimate of the corticomedullary sodium gradient. Potentially a voxel-by-voxel analysis along the corticomedullary axis could provide finer assessments of variations in the sodium gradient, but such an analysis was technically difficult given the relative small size kidneys in the juvenile pigs and the ROI analysis served as a straightforward analysis tool in our pilot study. Fourth, intravenous contrast material was administered to the pigs to provide a visual distinction between the location of the medulla and cortex for more precise placement of ROIs in the unenhanced CT images for our proof-of-concept study. In patients with renal insufficiency, however, administration of intravenous contrast material may be contraindicated. In those patients, the corticomedullary sodium gradient may be better measured using the pixel-by-pixel analysis of the image along the corticomedullary axis; the absolute differentiation between the cortex and the medulla may be unnecessary. This method was utilized in the analysis of the renal sodium gradient using sodium MR imaging in several published studies (6–9). Fifth, our institution does not currently own a dedicated DECT scanner, so we performed our DECT studies on a single-source CT scanner using the previously described rotate-rotate method (10). Though great care was taken to ensure that the consecutive scans at 80 and 140 kVp were taken in the same breath hold with no shift in animal position, it is possible that some slight misregistration may have occurred that may have affected the calculated medulla-to-cortex sodium ratios, and that use of newer DECT scanners will produce superior results. Sixth, histopathological analysis of the kidneys was performed in two of the four pigs. While we did not have histopathology evaluation for the other two pigs, presence of renal tubular injury in those two pigs was unlikely given the normal physiological response to saline and furosemide and the absence of known renal disease in these otherwise healthy animals.

Notwithstanding these limitations, we have shown that it is feasible to monitor dynamic changes in the renal corticomedullary sodium gradient using dual-energy CT in swine. Potentially, DECT can be used to assess renal sodium gradient in a variety of physiological and pathological conditions such as acute tubular necrosis.

Appendix

Appendix 1: Basis Material Decomposition Method

The sodium fractions in the renal medulla and cortex can be calculated from the CT numbers using the following equations.

The linear attenuation coefficient (μ) of a given object (kidney in this case) at a particular CT scanner may be determined using the following equation:

$$\frac{\mu -{\mu }_{H_{2}O}}{{\mu }_{H_{2}O}}•1000=HU,$$ (1)

where μ_H2O is a property of the CT scanner (0.2781/cm and 0.2273/cm at 80 and 140 kVp, respectively, for the scanner used in this experiment), and HU is the measured CT numbers in the renal medulla and cortex. In DECT, there will be two HU measurements (CT numbers) at two distinct tube energies e₁ (80 kVp) and e₂ (140 kVp). Thus, we can obtain μ(e₁) and μ(e₂) for a given object (kidney in this case) using equation (1) above. For this study, we will consider that the kidney is composed of sodium and renal soft tissue. The sodium fractions can then be calculated using the following equations:

$$1={\mathrm{f}}_{\mathrm{x}}+{\mathrm{f}}_{\mathrm{y}}$$ (2)

$$\mathrm{\mu }({\mathrm{e}}_1)={\mathrm{f}}_{\mathrm{x}}{\mathrm{\mu }}_{\mathrm{x}}({\mathrm{e}}_1)+{\mathrm{f}}_{\mathrm{y}}{\mathrm{\mu }}_{\mathrm{y}}({\mathrm{e}}_1)$$ (3)

$$\mathrm{\mu }({\mathrm{e}}_2)={\mathrm{f}}_{\mathrm{x}}{\mathrm{\mu }}_{\mathrm{x}}({\mathrm{e}}_2)+{\mathrm{f}}_{\mathrm{y}}{\mathrm{\mu }}_{\mathrm{y}}({\mathrm{e}}_2)$$ (4)

where f_x and f_y are the fractions of sodium and renal soft tissue respectively, μ_x(e₁) is the linear attenuation coefficient of sodium at 80 kVp and μ_x(e₂) is the linear attenuation coefficient of sodium at 140 kVp, μ_y(e₁) is the linear attenuation coefficient of renal soft tissue at 80 kVp and μ_y(e₂) is the linear attenuation coefficient of soft tissue at 140 kVp. Linear attenuation coefficients for sodium and renal soft tissue at 80 and 140 kVp were obtained from the National Institute of Standards and Technology database (20). For sodium, the linear attenuation coefficients are 1.8655/cm and 1.1235/cm at 80 and 140 kVp, respectively. For renal soft tissue, the linear attenuation coefficients are 0.2956/cm and 0.2402/cm at 80 and 140 kVp, respectively.

A non-negative least squares method was employed in MATLAB (Version 2008b, Mathworks, Natick, MA) to iteratively solve equations 2–4 for f_x (sodium fraction).

Appendix 2: Conversion of sodium fractions to sodium concentrations

The CT number attributed to sodium (HU_x) for a given region of interest (ROI) within the kidney may be determined using the following equation:

$${\mathrm{f}}_{\mathrm{x}}·\text{HU}={\text{HU}}_{\mathrm{x}}$$ (5)

where f_x is the sodium fraction calculated using equations in Appendix 1 above, HU is the measured CT number of the ROI at 80 kVp, and HU_x is the CT number attributed to sodium within the given ROI. HU_x may then be converted to sodium concentration using the following equation (6), which shows a linear correlation between CT number and sodium concentration. This relationship was empirically determined in a CT phantom of sodium chloride (18).

$${\text{HU}}_{\mathrm{x}}=0.1147·\mathrm{c}$$ (6)

where 0.1147 is the slope of the graph relating sodium concentration to CT number at 80 kVp and c is the sodium concentration in mmol/L.